# Mathematical relationship between velocity and distance

### what is the relationship between velocity and distance? | Yahoo Answers

Displacement is the vector difference between the ending and starting positions of an object. It may be very different from the distance the object has travelled. The relation between distance s and velocity v is given by v=s/(3+s). Find the acceleration in terms of s. In order to find acceleration, a = dv/dt. v = s / (3 +. Understand the RELATIONSHIPS between distance and time for constant and Understand the meaning of the slope and area of a graph of velocity vs. time .. between distance and the square of time in part C. The mathematical logic is.

What velocity is represented by the symbol v?

If you've been paying attention, then you should have anticipated the answer. It could be the velocity the meteor has as it passes by the moon, as it enters the Earth's atmosphere, or as it strikes the Earth's surface.

### Displacement and Velocity

It could also be the meteorite's velocity as it sits in the bottom of a crater. Are any of these the final velocity? Someone could extract the meteorite from its hole in the ground and drive away with it. Probably not, but it depends.

• Displacement and Velocity
• Discussion

There's no rule for this kind of thing. You have to parse the text of a problem for physical quantities and then assign meaning to mathematical symbols. The last part of this equation at is the change in the velocity from the initial value. Recall that a is the rate of change of velocity and that t is the time after some initial event.

Rate times time is change. Move longer as in longer time.

Acceleration compounds this simple situation since velocity is now also directly proportional to time. Try saying this in words and it sounds ridiculous.

### Sci Lab: Describing Motion

Would that it were so simple. This example only works when initial velocity is zero. Displacement is proportional to the square of time when acceleration is constant and initial velocity is zero. Your second point for the fast car is the velocity you measured.

## Distance, Velocity and Time: Equations and Relationship

Using your ruler and pencil connect the two points to make another line. Make this line look different than the first, either by making dashes or making it darker. Label the lines fast car and slow car. Find where the two lines cross. At this intersection point, trace one line to X axis, and another to the Y axis. These are the lines with arrows on diagram 1. The two values you see are the time and distance where the fast car should overtake the slower car.

Mark the predicting passing point on your course. Mark off the calculated point where the faster car should overtake the slower car.

Have your assistant release the slower car at the head start mark while you simultaneously release your faster car at the starting line. Start the timer a third person might be nice for this. Watch carefully to see where the fast car overtakes the slow car.

Compare your predicted time and distance that the fast car overtook the slower car with the actual values. Results Your results are likely to be pretty close to what your graph predicts, but they will likely vary depending on the velocities of your cars and whether or not they travel at a consistent velocity.

Conduct more trials if you wish. Uniform velocity is a linear function, making them easy and fun to predict. Although the slower car had a head start in distance, the faster car covered more distance in less time, so it caught up.

This is where the lines crossed. A non-graphical way of looking at this is using the following equation: The total distance each car travels to intersect is the same. Then, you can tell your parents how soon you will arrive at your destination.

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